Problem: Solve for $x$ and $y$ using elimination. ${x-4y = -7}$ ${-x+5y = 10}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {x-4y = -7}\thinspace$ to find $x$ ${x - 4}{(3)}{= -7}$ $x-12 = -7$ $x-12{+12} = -7{+12}$ ${x = 5}$ You can also plug ${y = 3}$ into $\thinspace {-x+5y = 10}\thinspace$ and get the same answer for $x$ : ${-x + 5}{(3)}{= 10}$ ${x = 5}$